Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).

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4
votes
2answers
1k views

How to find regions that satisfy this inequality?

I am new to Mathematica and would like to find the set $$\{ (x,y) \in \mathbb{R}^2: (3x+y\exp(xy))(x-a) + (6y + x \exp(xy))(y-b) < 0 \}$$ for some constants $a$ and $b$. How can I do ...
1
vote
1answer
415 views

General form of a linear transformation

Let $v_1 = \begin{bmatrix} 2 \\ -1 \end{bmatrix}$ and $v_2=\begin{bmatrix} 1 \\ -1 \end{bmatrix}$ and let $A= \begin{bmatrix} 3 & 2 \\ -2 & 1 \end{bmatrix}$ be a matrix for $T\colon \Bbb ...
13
votes
1answer
717 views

Nonlinear FEM Solver for Navier-Stokes equations in 2D

it's me again. I'm trying to obtain a numerical solution to Navier-Stokes equations in 2D in a non-rectangular region. So far, this guide was very helpful, but he is using finite differences, which is ...
9
votes
5answers
795 views

Create filling between two trig functions

Working with trig functions, period, amplitude, etc. I found a worksheet at a calculus website, with some nice questions related to interpreting trig functions, at least, they provide some "fun" ...
8
votes
3answers
1k views

Checking if the roots of a function are real

I'm trying to determine if the roots of a function are real. How would you do that? (In particular I'm interested in verifying that the roots of LegendreP[6, x] ...
3
votes
1answer
557 views

How do I solve $1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x))= 0$?

Consider the equation $$ 1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x)) = 0 $$ where $A,B \in \mathbb{R}$ are constants. What is the analytic solution?
9
votes
3answers
288 views

Labeling solutions of an Eigenvalue equation involving Bessel functions

I'm solving the Schrödinger equation for a particle in an annular geometry with hard wall boundary conditions and I've reduced it to the following equation: $$J_m(k\,R_1)\,Y_m(k\,R_2) - ...
7
votes
4answers
789 views

Solving $L=\frac{3}{2} \sqrt{4 \pi ^2 A^2+W^2}-\frac{\sqrt{5 W \sqrt{4 \pi ^2 A^2+W^2}+6 \pi ^2 A^2+3 W^2}}{\sqrt{2}}+\frac{3 W}{2}$ for $W$

When I solve the aforementioned equation for $W$ or $A$ on Mathematica I get a long and ugly equation in return, namely one of the solutions for $W$ is: (attempt to read at your own health) ...
7
votes
1answer
735 views

How to substitute the following conditions into an expression?

I have an expression: $p=a\;b\; x + b^2\; y + a\;c\; z$. I want to substitute $a\;b=1$, $b^2 = 2$ and $a\;c = 4$ to obtain $p = x + 2y + 4z$. How can I tell Mathematica to do that? I dont know how to ...
6
votes
4answers
439 views

Am I missing anything? Solving Equations

I want to know what $ a^4+b^4+c^4 $ would be when $ a+b+c=1, a^2+b^2+c^2=2, a^3+b^3+c^3=3. $ I tried ...
5
votes
2answers
2k views

Find all roots in range

Is there any way to check for all roots in a range? Jens' findAllRoots function is pretty good, but runs at approx. 10% of roots missed when I ran a quick check on ...
12
votes
3answers
445 views

FindInstance with a Diophantine equation seems to go on forever

I tried to find a non-trivial integer solution to the equation $$2012^2=a^2+b^2+c^2+d^2+e^2$$ with Mathematica but the computation takes minutes; I might be doing something wrong. ...
4
votes
1answer
217 views

How to speed up calculation of this equation (FindRoot)

I have come up with the following functions, and I need to calculate a value, in order to have a condition valid. In my problem, all data are given, and I need to calculate variable l. I am using ...
30
votes
2answers
2k views

The Orbit and Perigee of the Flamsteed comet

Historical context This year we have the 330-th anniversary of the Battle of Vienna - one of the great formative events of European history, it took place on September 12, 1683. Kara Mustafa, Grand ...
15
votes
3answers
525 views

Solving the magic backyard puzzle with MMA

I was trying to solve this puzzle using mma It looks like the generalization of the magic square. Anyway here my attempt:- There are four columns $(x,y,z,w)$ and nine rowa which are denoted by the ...
11
votes
3answers
911 views

Finding “Maxima” and “Minima” on a B-Spline

I need to find the "Maxima" and "Minima" on a B-Spline or more correct the points where the 2nd components of the derivate equal zero. For example: ...
14
votes
3answers
1k views

NSolve gives additional solutions that don't satisfy the equations!

I am trying to solve the following polynomial equations in Mathematica: ...
14
votes
3answers
414 views

Is there any predictor-corrector method in Mathematica for solving nonlinear system of algebraic equations?

The FindRoot Function in Matheatica can easily be used to solve systems of nonlinear algebraic equations. But, I want to solve a system of nonlinear equations with variations of some parameters. ...
12
votes
2answers
15k views

Figuring when the minute and hour hand coincide on a clock

I would like to list all possible times in a 12-hour period, where the hour hand overlaps the minute hand completely. This is really a question about three distinct things - to be done in Mathematica ...
6
votes
2answers
1k views

Solution of equation with power series (perturbation)

So I need to use Mathematica to find the solution of $y=x- \epsilon \sin(2y)$ as a power series in terms of $\epsilon$. I'd assume I'd need to create an equation $f=x-y- \epsilon \sin(2y)$, then ...
4
votes
3answers
1k views

Solving Integrals

Here's a problem that I don't understand. f[x_] := Exp[Cos[3*x]] g[x_] := (1/3)*x^3 - x^2 + 2 When I try to find the limit: ...
11
votes
5answers
8k views

How to get rid of warnings when using Solve on an equation with inexact coefficients?

When I solve this equation in Mathematica 8, I can get the right answer, but with some uncomfortable warnings. Equation: ...
8
votes
3answers
717 views

How do I make Reduce yield all solutions explicitly?

Say I want to do the following: Reduce[ x+y+z==1, {x,y,z}, Modulus -> 7 ] then I get a solution with parameters, C[1] : ...
3
votes
2answers
908 views

All possible solutions to the Matrix Equation (free variables appearing)

I am attempting to solve a system of linear equations using LinearSolve[] . In my case, the number of unknowns are more than constraints. I learnt that LinearSolve ...
5
votes
1answer
397 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
5
votes
2answers
333 views

Counting Real roots

I'm interested on how to count the number of real roots of a random polynomials in an instant, how to put the result in a table and how to plot it in a graph.I generated 1 million random polynomials ...
4
votes
4answers
4k views

Solving complex equations

I feel like I am missing a basic, but key point when using Mathematica's Solve or Reduce. ...
3
votes
1answer
634 views

FindRoot giving false roots with Bessel Functions

I have read in some places about the errors associated with FindRoot, but the closest thing I can find on this website seems to be due to the imaginary unit. I am dealing with what should be a ...
10
votes
3answers
390 views

Bug: Wrong results from NSolve on coupled polynomials. WorkingPrecision->Automatic fails

OP UPDATE: I received an email from WR on 1-18-2016: "...It does appear that the NSolve function is not behaving properly in this case and I have forwarded an incident report to our developers with ...
9
votes
4answers
261 views

How to find the next root larger than a specified value, numerically?

I would want to have a general-purpose, reasonably robust method of finding the next numerical root above a specific value of x. I'm stumped by the fact ...
8
votes
2answers
249 views

What are the Method options Solve command accepts?

What are the Method options Solve command accepts? Solve has the Method option, however documentation contains no methods that it accepts...
7
votes
3answers
564 views

NDSolve and {C, K, Slot} and other built-ins as a variable name

The following problem is an exploration of what causes the error "Input is not an ordinary differential equation" in Mathematica as it seems to have changed from version 8 to version 9. Specifically ...
4
votes
1answer
381 views

Eliminating functions from system of PDE in Mathematica

Mathematica users, Let's see an example of three PDEs: How can I eliminate variables q1[x,y,z] and q2[x,y,z] from a system of ...
4
votes
1answer
3k views

Finding the Minimum value of an interpolating function

I can't seem to use FindMinValue to find the min. value of a curve represented by an interpolating function. For instance the below code generates an interpolating ...
4
votes
3answers
2k views

Backsubstituting solution into FindRoot

I am trying to solve a system of equations which is dependent to an parameter alpha. So I iterate over alpha via a ...
3
votes
1answer
1k views

Solving a differential equation with initial conditions

I want to get a solution to an ordinary differential equation with imposed initial conditions. I'm confused about why my following code doesn't work: ...
0
votes
1answer
206 views
0
votes
1answer
202 views

How can I obtain the complex root of an equation with FindRoot

I want to obtain the complex roots of some equations that are similar,but each of them has a different condition. this difference is the value of α in these ...
0
votes
2answers
132 views

Gaps in plots of equation solution from parameter

I'm trying to plot solution of system of equations as a function of parameter ...
15
votes
2answers
4k views

FindRoot Domain restriction

I am solving a system of four non-linear equations in four variables using FindRoot. I have some sense of the relationship between the variables so I don't want Mathematica to do its computations in ...
14
votes
3answers
907 views

How can I simulate this toggle mechanism?

I've been introduced to Mathematica very recently. Basically, I haven't actually "solved" anything in my Mathematica lifetime, but I've done some simulations. With my fractional knowledge, I tried ...
9
votes
3answers
947 views

Implement the Bisection algorithm elegantly and easily

Description: Rencently, I have finished my course Numerical Analysis, so I'd like to implement many algorithm that I have learned from that course.By this practice, I hope that I can improve my ...
11
votes
3answers
976 views

How can we plot the complex roots of an equation?

If we'd like to display the $n$ roots of a polynomial on the complex plane as points, how can we do this? For example, if we have the equation $x^3 + x^2 + x + 1$, how can we plot the 3 roots as ...
6
votes
3answers
2k views

Why won't Mathematica Solve a set of two equations for one variable?

For example, if I try to Solve this set of equations Solve[y == 3 x + 5 && y == -x + 7, {x, y}] Mathematica gives the right values for ...
6
votes
2answers
2k views

How to invert an integral equation

There have been numerous times when I've needed to invert an integral equation, i.e. I have something like $$f(x) = g_1(x)\int_{0}^x g_2(x') dx'$$ for arbitrary functions $g_1$ and $g_2$, and ...
16
votes
2answers
296 views

How to implement Bresenham’s algorithm as a system of equations?

Bresenham's line drawing algorithm is usually implemented via loops. But in Mathematica we can take advantage of its ability to solve Diophantine equations. From educational viewpoint it is quite ...
7
votes
2answers
229 views

How to correct this, `f[a_] := FindRoot[eq == 0, {x, 0.5}]`, where `eq` contains a parameter $a$, without using `eq[a]`?

I want to solve an equation with a parameter $a$, and define the result as a function of $a$. It is something like this: ...
4
votes
1answer
2k views

Solve system of equations related to perspective projection

I'm trying to solve system of equations. I have 4 points before perspective projection and after and I whant to obtain matrix of perspective projection $m_{i,j}$ ($x,y,u,v$ are known , $m_{i,j}$ ...
2
votes
3answers
445 views

Solving an equation involving an integral

How do I get the following into Mathematica, solving for $a$: $$ 0.7 = 1 - \frac{2}{a} \times \left[ \frac{1}{a} \int_0^a \frac{x}{\exp(x)-1}\mathrm dx + \frac{a}{6} - 1\right] $$
2
votes
1answer
4k views

Forcing FindRoot to return only real solutions

FindRoot documentation reports that if the equation and the initial point are reals, the solutions are searched in the real domain. However, in the following case I ...